Applications of gauged linear sigma models
MetadataShow full item record
This thesis is devoted to a study of applications of gauged linear sigma models. First, by constructing (0,2) analogues of Hori-Vafa mirrors, we have given and checked proposals for (0,2) mirrors to projective spaces, toric del Pezzo and Hirzebruch surfaces with tangent bundle deformations, checking not only correlation functions but also e.g. that mirrors to del Pezzos are related by blowdowns in the fashion one would expect. Also, we applied the recent proposal for mirrors of non-Abelian (2,2) supersymmetric two-dimensional gauge theories to examples of two-dimensional A-twisted gauge theories with exceptional gauge groups G_2 and E_8. We explicitly computed the proposed mirror Landau-Ginzburg orbifold and derived the Coulomb ring relations (the analogue of quantum cohomology ring relations). We also studied pure gauge theories, and provided evidence (at the level of these topologicalﬁeld-theory-type computations) that each pure gauge theory (with simply-connected gauge group) ﬂows in the IR to a free theory of as many twisted chiral multiplets as the rank of the gauge group. Last, we have constructed hybrid Landau-Ginzburg models that RG ﬂow to a new family of non-compact Calabi-Yau threefolds, constructed as ﬁber products of genus g curves and noncompact Kahler threefolds. We only considered curves given as branched double covers of P^1. Our construction utilizes nonperturbative constructions of the genus g curves, and so provides a new set of exotic UV theories that should RG ﬂow to sigma models on Calabi-Yau manifolds, in which the Calabi-Yau is not realized simply as the critical locus of a superpotential.
General Audience Abstract
This thesis is devoted to a study of vacua of supersymmetric string theory (superstring theory) by gauged linear sigma models. String theory is best known as the candidate to unify Einstein’s general relativity and quantum field theory. We are interested in theories with a symmetry exchanging bosons and fermions, known as supersymmetry. The study of superstring vacua makes it possible to connect string theory to the real world, and describe the Standard model as a low energy effective theory. Gauged linear sigma models are one of the most successful models to study superstring vacua by, for example, providing insights into the global structure of their moduli spaces. We will use gauged linear sigma models to study mirror symmetry and its heterotic generalization “(0, 2) mirror symmetry.” They are both world-sheet dualities relating different interpretations of the same (internal) superstring vacua. Mirror symmetry is a very powerful duality which exchanges classical and quantum effects. By studying mirror symmetry and (0, 2) mirror symmetry, we gain more knowledge of the properties of superstring vacua.
- Doctoral Dissertations